HybridGNN: A Self-Supervised Graph Neural Network for Efficient Maximum Matching in Bipartite Graphs

Abstract

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel Graph Neural Network model designed to efficiently address complex matching problems at scale. HybridGNN leverages a combination of Graph Attention Networks (GATv2), Graph SAGE (SAGEConv), and Graph Isomorphism Networks (GIN) layers to enhance computational efficiency and model performance. Through extensive ablation experiments, we identify that while the SAGEConv layer demonstrates suboptimal performance in terms of accuracy and F1-score, configurations incorporating GATv2 and GIN layers show significant improvements. Specifically, in six-layer GNN architectures, the combinations of GATv2 and GIN layers with ratios of 4:2 and 5:1 yield superior accuracy and F1-score. Therefore, we name these GNN configurations HybridGNN1 and HybridGNN2. Additionally, techniques such as mixed precision training, gradient accumulation, and Jumping Knowledge networks are integrated to further optimize performance. Evaluations on an email communication dataset reveal that HybridGNNs outperform traditional algorithms such as the Hopcroft–Karp algorithm, the Hungarian algorithm, and the Blossom/Edmonds’ algorithm, particularly for large and complex graphs. These findings highlight HybridGNN’s robust capability to solve maximum matching problems in bipartite graphs, making it a powerful tool for analyzing large-scale and intricate graph data. Furthermore, our study aligns with the goals of the Symmetry and Asymmetry Study in Graph Theory special issue by exploring the role of symmetry in bipartite graph structures. By leveraging GNNs, we address the challenges related to symmetry and asymmetry in graph properties, thereby improving the reliability and fault tolerance of complex networks.